The truncation error for the sign magnitude representation is symmetric about zero and falls in the range

Since the binary digit b-A is the first bit in the representation of the real number, it is called as the most significant bit(MSB) of the number.

We can represent 5 as

For a two’s complement representation, the truncation error is always negative and falls in the range

The ones complement of (1100)2 is (0011)2. Thus the two complement of this number is obtained as (0011)2+(0001)2=(0100)2.

Let the mantissa be represented by 23 bits plus a sign bit and let the exponent be represented by 7 bits plus a sign bit.

A fixed point representation of numbers allows us to cover a range of numbers, say, xmax-xmin with a resolution

We can represent the numbers in binary float point as

Let us consider two numbers X=M.2E and Y=N.2F

In floating point representation, the mantissa is either rounded or truncated. Due to non-uniform resolution, the corresponding error in a floating point representation is proportional to the number being quantized.